Create Additional Curves Morphing Between 2 Input Curves
This will work only if both initial and final morphing shape have the same number of vertex.

If they don't you can always add a few more to the one with the least vertex, if moving them in place is not too much of a hassle.

Then create one single curve, shape it as desired.

Add two new Shapekeys to it, one Basis and one with the desired final morphing shape.

Now make a few copies of the curve (non-linked clones), and on each one gradually increase the Value for the shapekey.

For an even constant morphing divide the percentage by the number of "snapshots" you plan to have.